A Numerical Solver for First Order Initial Value Problems of Ordinary Differential Equation Via the Combination of Chebyshev Polynomial and Exponential Function

Abstract

Purpose: The purpose of this study is to derive a numerical solver for first order initial value problems of ordinary differential equation via the combination of Chebyshev polynomial and exponential function.Methodology: A new numerical method for solving Initial Value Problems of first order ordinary differential equation is developed. The method is based on finite difference method with a combination of Chebyshev polynomials and exponential function as interpolant. The accuracy, stability, consistency and convergence of the derived scheme were investigated. Numerical experiment was carried out by solving some test problems using the derived scheme.Findings: Results of the numerical experiment revealed that the derived method compared favourably with exact solutions and also performs better than some existing methods for solving initial value problems of first order. Unique Contribution to theory, practice and policy: The study therefore concludes that the method solves problems to expected level of accuracy and can thus be considered among the numerous methods suitable for solving IVPs of first order.